1. Field of the Invention
The field of the present invention is sample data creation from computerized modeling, particularly where the computerized model is based upon a mass, or a portion of a mass, and is usable as a tool to indirectly examine the mass through the use of acoustics.
2. Background
Computerized modeling is used in many different disciplines for different purposes. One use of computerized modeling is to identify the interior features of a mass. The mass may be any volume having features of interest which are not readily discernable because they are hidden from direct observation. Instead, the features of interest are susceptible to indirect methods of examination using acoustics. For example, in geophysics, the mass may be an oil well, a water table, or any other geophysical feature. In medicine, the mass is a human or animal body.
To identify physical features within the mass, it is well known to direct acoustic energy into the mass and to collect data as the acoustic energy emerges from the mass. That acoustic data, together with other sources of information, may be used to construct an initial computerized model of the mass. The process of creating the computerized model is commonly known as imaging or inversion. Once the computerized model is constructed, it may be used to obtain simulated data. The simulated data is then compared to the actual data obtained from the mass to determine the accuracy of the model.
The simulated data is most often obtained by finding a numerical solution to the acoustic wave equation using different approximation methods. One such approximation method is commonly referred to as high frequency approximation, or ray tracing. Ray tracing is found in everyday engineering and scientific community across disciplines, especially those in optics and in acoustics. It is based on the geometrical optics high temporal frequency approximation that the size of the object is much greater than the wavelength of propagation. For applications in which such approximations are not valid, the ray tracing solution produces non-physical caustics, singularities, and shadow zones. Further, for applications in which solutions are desired for a wide range of temporal frequency values, the ray tracing method has questionable value.
A second approximation method is commonly referred to as parabolic approximation, or a one-way wave equation. This method can also be found in many scientific and engineering disciplines, and is particularly useful for those instances in which the effects of backscattering can be neglected. Such approximations are valid for most optical propagation and underwater acoustics applications. However, the accuracy of such approximations is questionable in most geophysical applications and in other acoustical problems such as ultrasound propagation through human tissues.
Other solution methods exist, such as the small perturbation method, but such methods are generally problem specific. They are therefore of little value as a solution for acoustic wave propagation in a general medium and for arbitrary temporal frequencies.
The acoustic wave equation can also be solved in the time-domain to obtain the time-evolution effects. For problems in an infinite physical domain, this method suffers from difficulties in absorbing boundary conditions. Further, there is the added difficulty of dealing with wave propagation in a high contrast medium. The same problems arise when using the spatial Helmholtz equation.
The Helmholtz equation approach is most suitable for inversion/imaging applications. Full waveform imaging/inversion uses all the time series data at the sensor locations. The difficulty with the high temporal frequency approximation is that not all of the sensed data can be readily utilized.
In short, the state of the art for solving a time-dependent wave equation is both resource taxing and time consuming. Each of the aforementioned methods, i.e. ray tracing, the parabolic wave equation, and the Helmholtz reduced wave equation, has limitations which limit real-world applications for computerized modeling using acoustics.